## An Hélein’s type convergence theorem for conformal immersions from $\mathbb {S}^{2}$ to manifold

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**147**(2019), 4969-4977 Request permission

## Abstract:

In this short paper, we establish an Hélein’s type convergence theorem for conformal immersions from $\mathbb {S}^{2}$ to a general compact Riemannian manifold. As an application, we extend the existence of minimizer of $\int |A|^{2} d\mu$ for immersed 2-spheres in compact 3-manifolds under certain conditions due to E. Kuwert, A. Mondino, and J. Schygulla to higher codimensions.## References

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## Additional Information

**Guodong Wei**- Affiliation: Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
- Email: weiguodong@math.pku.edu.cn
- Received by editor(s): November 19, 2018
- Received by editor(s) in revised form: February 24, 2019
- Published electronically: June 10, 2019
- Additional Notes: This work was supported by National Natural Science Foundation of China (Grants No. 11671015 and 11731001).
- Communicated by: Guofang Wei
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 4969-4977 - MSC (2010): Primary 53C42; Secondary 53A30, 53A07
- DOI: https://doi.org/10.1090/proc/14614
- MathSciNet review: 4011528